Los Angeles, CA ▪ San Francisco, CA ▪ Tallahassee, FL ▪ Washington, DC © 2011, ERSGroup

Regression Analysis Applications in Litigation

By

Robert Mills

Director

Micronomics, Inc.

Dubravka Tosic, Ph.D.

Principal

ERS Group

Practising Law Institute

Pocket MBA: Finance for Lawyers

Summer 2011

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Regression Analysis Applications in Litigation

Robert Mills*

Dubravka Tosic, Ph.D.**

March 2011

I. Introduction to Regression Analysis

Regression analysis is a statistical tool used to examine

relationships among variables. It provides a method for

quantifying the impact of changes in one or more explanatory

variables (known as independent variables) on a variable of

interest (known as the dependent variable). Regression analysis is

widely used in the field of econometrics, which is concerned with

the application of statistical and mathematical methods to the

analysis of economic data.1 Useful applications also are found in

finance, sociology, biology, psychology, pharmacology, and

engineering, among other fields of study. In this paper, we provide

an introduction to regression analysis and discuss a number of

applications in the litigation context.

Regression analysis begins with a hypothesis. Suppose, for

example, that we are interested in understanding factors that

impact attendance at a sporting event. We might hypothesize that

historical performance of the home team influences attendance.

* Robert Mills is a Director at Micronomics, Inc., an economic research

and consulting firm in Los Angeles, California. Micronomics is a

subsidiary of ERS Group, a national economic and statistical consulting

firm. **

Dubravka Tosic, Ph.D. is a Principal at ERS Group, and based in New

York/New Jersey. 1 Additional information can be found in an econometrics textbook such

as James H. Stock and Mark W. Watson, Introduction to Econometrics,

3rd ed. (Upper Saddle River: Prentice-Hall, 2010); William H. Greene,

Econometric Analysis, 7th ed. (Upper Saddle River: Prentice-Hall, 2011);

or Peter Kennedy, A Guide to Econometrics, 5th ed. (Cambridge: The

MIT Press, 2003).

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We might further believe that the relationship between historical

performance and attendance is positive; that is, improvements in

performance of the home team lead to greater attendance and

declines in performance of the home team lead to lower

attendance. Assuming historical attendance and home team

performance data are available, we can estimate the following

model:

where

= attendance at game i (the dependent variable);

= home team performance as of game i measured by the

win-loss record expressed as a percentage (the

independent variable);

= constant amount (interpreted as attendance given a

win-loss record of zero percent);

= the effect in attendance of each additional percentage

in the home team win-loss record; and

= a “disturbance” term reflecting other unmeasured

factors that influence attendance.

Data for A and P are plotted in the following figure. The

coefficients and are not known. Regression analysis produces

estimates for these coefficients, which customarily are denoted

with a “hat” superscript (e.g., and ). The disturbance term, ,

also is unknown.

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Graphically, estimation of the coefficients and is tantamount

to fitting a line to the attendance and home team win-loss record

data, where is the point at which the line intersects the vertical

axis and is the slope of the line. The following figure depicts

such a line.

This line appears to fit the data. Without an objective criterion,

however, there is no guarantee that this line provides the best fit.

Regression analysis provides a criterion. With regression analysis,

Att

end

ance

Home Team Win-Loss Record (%)

Att

endan

ce

Home Team Win-Loss Record (%)

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the intercept and slope of the line (i.e., and ) typically are

estimated by minimizing the sum of squared errors (“SSE”).

First, an estimated error for each observation is measured as the

vertical distance between the observed value of the variable and

the estimated line. SSE is calculated by squaring this estimated

error for each observation and summing across all observations.

Estimates of the coefficients are chosen to minimize SSE. This is

called the method of ordinary least squares. In practice, this

estimation is carried out using regression software. With ordinary

least squares the best fitted line for the data is estimated.

Common knowledge suggests that attendance at sporting events

increases with improvements in home team performance. In other

words, we expect a positive coefficient for home team win-loss

record ( indicating that attendance increases as performance

improves and attendance decreases as performance declines, other

things equal.

Estimating our model produces the following results.

Regression Output

R2 = 0.70

Coefficient

Standard

Error

t-Statistic

Intercept ( 25,419 4,913 5.17

Win-Loss Record ( ) 501 90 5.55

The estimated coefficient for the home team win-loss record is

501, which is interpreted as the estimated number of additional

attendees for every one percent improvement in the home team

win-loss record. This estimate is consistent with our expectation

that the coefficient is positive. The intercept term is interpreted as

the estimated number of attendees given a home team record of

zero wins. Using these coefficient estimates, attendance can be

predicted for any given home team win-loss record. For example,

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if the win-loss record is 50% as of game i, estimated attendance at

game i is

50,469 = 25,419 + (501 * 50).

The model suggests attendance would increase to 62,994 in the

event that the home team win-loss record improved to 75%:

62,994 = 25,419 + (501 * 75).

The results of the regression analysis appear to confirm our a

priori belief that attendance increases with improvements in home

team performance. Using the t-statistic reported above, we can

formally test the hypothesis that performance does not impact

attendance. Operationally, this test involves comparing the

reported t-statistic for the coefficient of interest to the critical value

obtained from the t distribution. Courts have frequently adopted

the concept of statistical “significance” when assessing the

importance of a variable. Assuming a large sample size, the critical

value is 1.96 (or approximately two standard deviations) at the five

percent level of significance. Since the reported t-statistic of 5.55

exceeds the critical value of 1.96, we can reject the hypothesis that

performance does not impact attendance at a five percent level of

statistical significance.

Another useful statistic frequently reported with regression results

is the coefficient of determination, or R-squared (R2). R

2 reflects

the proportion of total variation in the dependent variable

explained by variation in the independent variable or variables. In

other words, it provides a measure of the “explanatory power” of a

model.

The value of R2 ranges from 0 to 1, with a value of 0 meaning that

none of the variation in the dependent variable is explained by

variation in the independent variables and a value of 1 signifying

that all of the variation in the dependent variable is explained by

variation in the independent variables. Roughly speaking, a high

value of R2 often is associated with a good fit of the regression line

whereas a low value of R2 is associated with a poor fit. This does

not mean, however, that the relative strength of two competing

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models can be assessed by their respective R2 values alone. Indeed,

introducing additional independent variables into a model will tend

to increase the value of R2 even where those variables have no

hypothesized relationship with the dependent variable.

Specification of the regression model should be founded in theory.

Explanatory variables should not be included in a model without a

theoretical basis for inclusion. Similarly, explanatory variables that

theory suggests are relevant should not be excluded without a

sound basis for doing so. The exclusion of relevant explanatory

variables from a model without basis is particularly problematic

because it can lead to omitted variable bias.

Omitted variable bias arises when one or more variables that

should be included in a model are excluded from the estimated

model. In such cases, coefficient estimates for the included

variables can be biased and the results of hypothesis tests rendered

unreliable.2

Turning back to the sporting event attendance example, the only

explanatory variable we have considered is home team

performance as measured by the home team win-loss record.

Clearly, this is an overly simplistic view of the determinants of

attendance. Attendance likely is affected by a variety of factors in

addition to home team performance. Economic theory suggests, for

example, that ticket sales depend in part on ticket prices. The win-

loss record of the visiting team, the number of games left in the

season, the day of the week on which the event occurs, and game

day rainfall (particularly for outdoor events) might also be

relevant. Each of these variables is subject to measurement and

could be included in the model. The problem of omitted variable

bias is more troublesome when the omitted variable is not readily

subject to measurement and therefore cannot be included.

The problem of including irrelevant variables typically is less

serious than the problem of omitting relevant variables because the

2 Coefficient estimates for included variables will remain unbiased in the

event that the omitted variable is uncorrelated with all of the included

variables.

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inclusion of irrelevant variables does not serve to bias estimates of

the coefficients for relevant variables. This is not to say that the

practice of including irrelevant variables in a model is without

cost. The efficiency of the estimator is affected by including

irrelevant variables, which can be problematic particularly when

working with small sample sizes.

While identifying relevant explanatory variables is an essential

aspect of model specification, the choice of functional form also is

important. Thus far we have assumed that the relationship between

the dependent variable and the independent variables is linear.

Depending upon the application, theory may suggest that a

nonlinear functional form is more appropriate. The left and right

panels of the following figure illustrate nonlinear functional forms

commonly used in practice. The left panel depicts a semi-log

model and the right panel depicts a polynomial model.

Many nonlinear functional forms, including those shown above,

can be estimated using standard linear regression techniques

because they are linear in the coefficients. Nonlinear functional

forms that are not subject to linear transformations require more

sophisticated estimation techniques.

There are a number of assumptions that underlie the standard

linear regression model. It is important to recognize situations

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where these assumptions are violated so that alternative methods

can be employed to produce sound results. It is beyond the scope

of this paper to provide a comprehensive overview of all of the

problems that can arise. Instead, we will focus on two common

problems that are related to the disturbance term.

It typically is assumed that the disturbance term is composed of

small, individually unimportant effects that are independently

distributed from a normal population with an expected value of

zero and constant variance.

Violations of the constant variance assumption are not uncommon

in practice. When working with data from a cross section of firms

in an industry, for example, a systematic difference between the

disturbances for large and small firms may exist indicating that

variance of the disturbance term is not constant. Disturbances are

said to be heteroscedastic when they have different variances.

Violations of the independence assumption sometimes arise when

working with time series data because the disturbance associated

with observations for one period may carry over into future

periods. Disturbances are said to be serially correlated when the

disturbance terms for different observations are correlated.

In the presence of heteroscedasticity or serial correlation, the

method of ordinary least squares produces coefficient estimates

that are unbiased but not efficient. The loss of efficiency is

undesirable because it can affect the results of hypothesis tests.

Fortunately, procedures for identifying and correcting problems

associated with heteroscedasticity and serial correlation are readily

available.

II. Examples of Practical Applications of Regression Analysis

The discussion thus far is intended to provide non-practitioners a

brief introduction to regression analysis. We now introduce some

practical applications of regression analysis in the litigation

context. Specifically, we provide an overview of (A) the role of

regression analysis in estimating price elasticity of demand in

antitrust and intellectual property matters, (B) use of regression

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analysis to conduct event studies designed to estimate the impact

of specific events on the value of a firm, (C) the application of

regression analysis to cost estimation in damages studies, and (D)

applications of regression analysis in labor and employment

disputes.

A. Price Elasticity of Demand

Demand refers to the quantity of a good or service consumers

purchase at prevailing prices. Increases in the prevailing price of a

good tend to result in reduced sales volume because some

consumers will choose alternative products or refrain altogether

from making a purchase as price increases. Conversely, decreases

in the prevailing price tend to result in sales volume increases. The

term price elasticity of demand refers to the extent to which sales

volume is affected by price changes.

Own-price elasticity of demand measures the responsiveness of the

quantity of a good demanded to changes in its price. Demand is

said to be elastic if quantity demanded is highly sensitive to

changes in price, and inelastic if price changes have little impact

on quantity demanded. Cross-price elasticity of demand measures

the responsiveness of quantity demanded for one good to changes

in the price of another good.

Own-price elasticity of demand is negative since price increases

lead to decreases in quantity demanded. This elasticity commonly

is reported in terms of absolute value, however, and the negative

sign can be assumed. Cross-price elasticity of demand can be

positive or negative depending upon whether the goods are

substitutes (positive cross-price elasticity) or compliments

(negative cross-price elasticity). Together, own- and cross-price

elasticity summarize anticipated substitution patterns among

consumers faced with changes in price.

The concept of price elasticity of demand has been widely used in

litigation, notably in assessing potential anticompetitive effects of

mergers. Own- and cross-price elasticity are routinely used to

define relevant antitrust markets, assess market power, and

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simulate price increases resulting from mergers before they are

consummated.

Use of price elasticity of demand also has emerged in patent

infringement litigation, particularly in cases where price erosion is

alleged to have occurred. An assessment of price erosion involves

estimating the price that would have prevailed but for the

infringement and then determining the amount of sales the patent

owner would have made at that price. Although a patent owner

may have been able to charge a higher price in the absence of the

infringement, its sales might have been lower depending upon the

price elasticity of demand.

Measures of price elasticity of demand commonly are derived by

estimating one or more demand curves using regression analysis.

Economic theory suggests the quantity of a good demanded

depends upon its price, the price of substitutes and complements,

and income, among other possible factors. In practice, data

limitations may dictate which variables are included in a regression

analysis, but the potential for omitted variable bias also should be

considered when specifying models.

Suppose we have monthly data on the quantity of goods sold (

and ) and corresponding price data ( and ) for two substitute

goods. We also have monthly income data (I) for consumers that

purchase the goods. We can estimate the following linear demand

equations using regression analysis.

We use a linear demand model in this example for simplicity.

Economic theory does not dictate an exact functional relationship

between quantity demanded and the variables that impact demand.

The properties of a specific functional form may lead the

researcher to believe it superior for a given situation, but the

choice is often somewhat arbitrary. If sufficient data are available,

a variety of functional forms might be estimated to assess the

sensitivity of the results to the choice of functional form. This

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practice may lend credibility to the results if they are shown to be

insensitive to the choice of functional form. Results that are

extremely sensitive to functional form may prove difficult to

defend.

Price elasticity for both goods can readily be estimated using the

estimated coefficients from the linear demand model. Own-price

elasticity is equal to the “first partial derivative” of the demand

equation with respect to price times price divided by quantity.

In other words, own-price elasticity of demand is equal to the

coefficient for the price variable multiplied by price which is

divided by quantity. Cross-price elasticity of demand is calculated

as the coefficient for the price of the other good multiplied by the

price of the other good divided by quantity.

Price elasticity estimates can prove useful in the litigation context,

particularly in cases where the interplay between price and

quantity is an issue. In antitrust litigation, for example, elasticity

and cross-price elasticity are often used to delineate relevant

markets. Firms are likely to be grouped in the same market if the

products they produce can be used interchangeably and where the

products exhibit a high cross-price elasticity of demand. In cases

where price allegedly would have been higher (or lower) in the

absence of some conduct, elasticity estimates can be used to show

the impact of that but-for price on quantity demanded.

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B. Event Study Analysis

Event studies measure the impact of specific events on the value of

firms. There are many useful applications for event studies in

litigation settings. For example, event studies are commonly used

to estimate the impact of adverse information on movements in

share prices in matters of alleged securities fraud. They also can

provide insight into damages resulting from events such as product

recalls, the loss of patent protection, credit facility constraints, and

fraud.

The basic premise underlying an event study analysis is that given

rational market participants, security prices will quickly adjust to

reflect the announcement of an event. Roughly speaking, security

price changes are attributable to company-specific information

(such as the announcement of a new product) and industry or

market-wide information (such as new regulation or changes in

interest rates). Event study analysis provides a framework for

isolating the impact of company-specific events on security prices.

The total impact of an event can then be estimated by summing the

company-specific impact across all of shares affected.

The first step in undertaking an event study analysis involves the

identification of the event or events of interest. In the litigation

context, the events of interest often are dictated by allegations in

the complaint. Suppose, for example, that a publicly traded early-

stage pharmaceutical company alleges that clinical trials for a

potential new therapeutic drug were unsuccessful as a result of a

failure on the part of its development partner to design a proper

test protocol. In this example, the event of interest is the public

announcement that the clinical trials were unsuccessful.

After the event of interest has been identified, it is necessary to

determine the period of time over which the impact will be

measured. This is called the event window. In practice, the event

window typically is defined to include at least the day on which

the event was announced and the following business day.

Depending upon the circumstances, the event window may

commence before the event is announced (e.g., if there is reason to

believe that news of the event leaked before the official

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announcement) and end days after the event is announced (e.g., if

there is reason to believe that some market participants did not

immediately learn of the event at the time it was announced). The

event window ideally will be long enough to include any ongoing

adjustment to news of the event in the market, but not so long as to

capture effects of unrelated subsequent events.

A primary objective of event study analysis is to isolate the impact

of the event in question from market-wide and industry-wide

information that also impacts securities prices. The following

model is often used in this context:

where

the security return on day t for the company of

interest;

the market index return on day t;

the intercept coefficient;

the market index coefficient; and

a disturbance term reflecting other factors that

influence the security return for the company of

interest.

Historical stock price data for the company in question are

collected and daily returns are calculated. Market index data also

are collected. This market index may be a widely available index

such as the Standard and Poor’s 500 or a custom index that

includes peers of the company of interest. Returning to our early-

stage pharmaceutical company example, a useful market index

might be constructed to include other publicly traded early-stage

companies involved in clinical trials for potential new therapeutics.

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Regression analysis is employed to obtain estimates for and .

The results of the regression analysis are then used to calculate the

predicted security return, for each day in the event window:

.

The predicted security return is essentially an estimate of the

security return but for the event in question. Predicted security

returns are compared to actual returns to determine the impact of

the event in question. The difference between the actual and

predicted return on any particular day is called the abnormal

return:

abnormal return .

Summing abnormal returns across all days in the event window

yields cumulative abnormal returns:

cumulative abnormal returns

Cumulative abnormal returns (or CAR) speak to the magnitude of

the event in question.

Event studies can also shed light on the materiality of events.

Materiality is addressed using statistical testing. A common

question in event studies is whether or not the hypothesis that the

cumulative abnormal returns are zero can be rejected. Output

obtained from the regression analysis provides the information

necessary to conduct such a test.

Event study analysis has been used in a wide range of

investigations. In the litigation context, it is used to estimate

damages caused by securities fraud and other wrongful conduct.

Event studies have also been used to understand the value created

by mergers and acquisitions, the impact of corporate earnings

restatements, and market reactions to jury verdicts.

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C. Cost Estimation in Damages Studies

In many cases, lost profits damages are calculated as the difference

between profits that would have been generated but for some

alleged conduct, such as a breach of contract, and actual profits

generated given the conduct. Estimating but-for profits requires an

understanding of the costs involved, and in particular those costs

that were not incurred given the alleged conduct but would have

been incurred in the absence of the alleged conduct. These costs

are sometimes referred to as avoided costs. The estimation of

avoided costs often requires an understanding of the distinction

between those cost elements that are fixed and those that are

variable.

Fixed costs do not vary with levels of output. Costs that frequently

are fixed over moderate changes in output include rent, insurance

premiums, business license fees, and salaries for permanent full

time employees.

Variable costs are those that vary directly with the level of output.

Depending upon the nature of the business, variable costs may

include cost of goods sold, shipping charges, royalties, and sales

commissions, among others.

Certain costs cannot be classified as strictly fixed or variable.

These semi-variable costs include a mixture of fixed and variable

components. Common examples of semi-variable costs include

production labor (regular wages are fixed but overtime is variable),

electricity, telephone bills, and postage.

An important consideration when assessing the nature of costs is

that cost elements can be fixed over certain levels of output and

variable over other levels of output. To illustrate this point,

suppose a manufacturer has the capacity to increase production by

ten percent without expanding its plant, but any increase in

production above ten percent would require an expansion. In this

example, the rent associated with the plant is fixed over relatively

small increases in output. Increasing output by more than ten

percent, however, would require an expansion of the plant and the

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payment of additional rent. In other words, rent is a variable cost in

this example over large increases in output.

Discussions with company management and accounting personnel

can be helpful in understanding the fixed or variable nature of

costs. Depending upon the availability of data, regression analysis

may provide additional insight.

Regression analysis provides a means to examine and quantify

relationships among variables. In the case of cost estimation, a

common inquiry is “what is the relationship between changes in

output and the cost of production?” Assuming sufficient data are

available, the following model might be estimated to address this

question:

where

= cost of production during period t;

= production during period t;

= the intercept coefficient;

= the production coefficient; and

= a disturbance term reflecting other factors that

influence the cost of production.3

The coefficient is interpreted as the cost of production when

output falls to zero units. In other words, it provides an indication

of the fixed cost of production. The coefficient is interpreted as

the cost of production for one additional unit of output. That is, it

provides an indication of the variable cost of production. Together,

3 Depending upon the situation, model specification might be more

complicated in practice. Decisions concerning the variables to include,

functional form, and data aggregation are driven by the specific facts and

circumstances of the investigation.

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these coefficients can be used to estimate the total cost of

production for a given level of output.

In our example, the regression results might be used to calculate

profit but for the alleged conduct:

Profit Sales Price .

Subtracting actual profits from but-for profits would yield an

estimate of profits lost as a result of the alleged conduct.

D. Labor and Employment Litigation

Almost all employers face federal nondiscrimination requirements,

and most states also have enacted employment laws specifically

dealing with discrimination. These federal and state laws are

intended to ensure that employers base employment practices (e.g.,

hiring, promotion, termination, discipline, compensation) on

objective and fair measures, such as performance and merit.

Employment discrimination allegations often charge employers

with engaging in discrimination against a member or members of a

protected class (legally protected characteristics include race,

gender, ethnicity, national origin, religion, age, and disability).

These allegations require plaintiffs to demonstrate that a pattern or

practice of discrimination exists. Statistical analysis is commonly

used to analyze such allegations. Various statistical tests can be

performed utilizing human resources, payroll, and other business

data. Regression analysis can also be employed to identify patterns

in data that reflect employment decisions.

Regression analysis may be viewed as a tool that quantifies the

relationship between a decision variable and other independent

factors. For example, suppose a company faces an employment

discrimination matter in which plaintiffs allege that women are

being discriminated against in terms of base pay. The hypothesis

we would want to test with regression analysis is that gender is not

a significant factor in determining the base salary level of

employees. The following multiple regression model could be

estimated:

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where

base salary for employee n;

characteristics of employee n;

gender of employee n;

the intercept coefficient;

the employee characteristics coefficients;

the gender coefficient; and

a disturbance term reflecting other factors that

influence base salaries.

This model is referred to as a multiple regression model since

multiple explanatory variables are considered. In our example, the

dependent variable is base salary and the independent variables are

various characteristics of employees that might influence base

salary and for which data are available. The employer might

contend that the following employee characteristics are important

determinants of base salary, and as such should be included in the

regression model: education, prior experience, tenure, special

skills, department, and geographic region. To test the hypothesis

that base salary for women is not different than the base salary for

men after controlling for all of these factors, the regression model

would also include a variable that reflects the gender of the

employee, which is depicted in our model as G. The constant term,

, is interpreted as the average base salary paid to a man who has a

zero value in each independent variable (e.g., no education, no

prior experience, and no tenure). The coefficients and measure

the influence of the independent variables on base salary.

Estimates of these coefficients are referred to as unbiased estimates

of the influence of the independent variables on the dependent

variable if the variables are independent of each other, no

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important variables have been omitted, base salary is normally

distributed, and other assumptions underlying the method of

ordinary least squares hold.

The difference between average base salary for men and women is

estimated by the coefficient . If this coefficient is statistically

significant (i.e., it has a t-statistic of more than 1.96 assuming a

five percent level of statistical significance), the difference

between the base salary for men and women is said to be

statistically significant after accounting for other factors included

in the regression model. Assuming the regression model controls

for factors influencing pay, this result would prompt us to reject

the hypothesis that gender is not a significant factor in determining

base salary.

Given the widespread availability of computing power and

sophisticated computer software, it is possible to generate a wealth

of information useful for identifying and examining outliers,

testing the robustness of models, and analyzing the sensitivity of

results to assumptions made. For instance, significant outliers are

often examined to further evaluate the quality of the model and

data. Using the base salary example provided above, data

pertaining to employees that are identified as statistically

significant positive or negative outliers (i.e., employees whose

actual base salary is significantly higher or lower than their

predicted base salary), could be reviewed to identify potential

anomalies in the data. This process can provide information that

might be used to further refine the model.

III. Conclusion

Implementing regression analysis requires an appreciation for the

statistical underpinnings of the analysis along with a well-designed

model that is founded in theory. When used properly, regression

analysis is a powerful tool with many practical applications in

litigation. It has been widely accepted by courts as a reliable

estimation framework.

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About the Authors

ROBERT MILLS is an economist and Director at Micronomics,

Inc., an economic research and consulting firm located in Los

Angeles, California. Micronomics, Inc. is a subsidiary of ERS

Group, a national economic and statistical consulting firm.

Mr. Mills has been engaged in economic research and consulting

for the past 15 years. A significant portion of his professional

experience has involved the valuation of intellectual property and

other assets, industrial organization, and the calculation of

economic damages. His experience spans many industries,

including software, semiconductors, health care, medical devices,

pharmaceuticals, entertainment, telecommunications, real estate,

apparel, manufacturing, retail sales, insurance, sporting goods, and

energy, among others.

Mr. Mills has served as an expert witness or consultant in a wide

range of matters, including patent, trademark and copyright

infringement, theft of trade secrets, breach of contract,

interference, conversion, fraud, predatory pricing, attempted

monopolization, and labor disputes. He has testified as an

economic expert in Federal District Court, state courts in multiple

jurisdictions, and at arbitration.

Mr. Mills also engages in economic research and consulting

outside the context of litigation. He has assessed the anticipated

competitive effects of mergers and joint ventures on behalf of

government regulatory agencies and merging parties; developed

forecasts and strategic recommendations for government agencies

and clients involved with real estate development; and assisted

clients with the valuation of intangible assets and entire businesses.

Mr. Mills received a Bachelor of Science degree in economics and

history from Portland State University and a Master of Arts degree

in economics from the University of California at Santa Barbara.

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About the Authors

DUBRAVKA K. TOSIC is an Economist and Principal at ERS

Group, a national leader in economic and statistical consulting.

She rejoined ERS Group in Spring 2010, after 12 years as a

Director in the Dispute Analysis practice of

PricewaterhouseCoopers, LLP in New York. Dr. Tosic has a

wealth of experience in leading and managing projects for private

and public sector clients, and their in-house and outside counsel,

involving economic and quantitative analyses and damage

calculations in a wide variety of complex disputes, litigation and

arbitration matters, and pro-active risk management and

compliance reviews.

Dr. Tosic’s primary areas of expertise are labor and employment

(employment discrimination litigation involving various employer

actions (e.g., hiring, promotion, termination), compensation

studies, reductions-in-force analyses, and wage and hour litigation)

and complex commercial litigation and disputes. She has provided

assistance as consulting expert or testifying expert to address

issues of class certification, liability, and estimated damages.

Additionally, Dr. Tosic has performed pro-active risk management

and compliance reviews, and management consulting projects

involving high-profile reform and transformational initiatives

involving process reviews and data analytics.

Dr. Tosic received her Ph.D. in economics from Florida State

University and her Bachelor’s degree from University of

Maryland, and previously worked at ERS Group from 1991-1996.

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About ERS Group

ERS Group is the preeminent economic and statistical consulting

firm for analyses related to employment matters. Founded in 1981,

with offices in Tallahassee, Washington, D.C., San Francisco, and

Los Angeles, its statistically sound studies provide clients with a

better understanding of their organizations and decision-making

processes. Its research has been used by clients in high stakes

employment litigation and regulatory matters involving allegations

of discrimination in hiring, promotion and compensation. ERS

Group’s national reputation is founded on the unparalleled

experience of its economists and testifying experts. Its reach

extends to more than 3,000 clients, including Fortune 500

companies, prominent law firms, universities, government

agencies, and industry trade associations. Its experts also have

been asked to share their experience and knowledge with

regulatory agencies such as the Office of Federal Contract

Compliance and the Equal Employment Opportunity Commission.

About Micronomics

Micronomics is an economic research and consulting firm located

in Los Angeles, California. Founded in 1988, it is engaged in the

application of price theory, analysis of issues relating to resource

allocation, and assessment of real-world problems requiring

practical and sound solutions. Micronomics focuses on industrial

organization, antitrust, intellectual property, the calculation of

economic damages, employment issues, and the collection,

tabulation, and analysis of economic, financial and statistical data.

Clients include law firms, publicly and privately held businesses,

and government agencies. In January 2011, Micronomics joined

ERS Group.